<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-09-23</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001589526</issuerCik>
        <issuerName>Blue Bird Corp</issuerName>
        <issuerTradingSymbol>BLBD</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001409751</rptOwnerCik>
            <rptOwnerName>Coliseum Capital Management, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>105 ROWAYTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001430708</rptOwnerCik>
            <rptOwnerName>Shackelton Christopher S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>105 ROWAYTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001409585</rptOwnerCik>
            <rptOwnerName>Coliseum Capital, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>105 ROWAYTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001356974</rptOwnerCik>
            <rptOwnerName>COLISEUM CAPITAL PARTNERS, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>105 ROWAYTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001567187</rptOwnerCik>
            <rptOwnerName>Coliseum Capital Partners II, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>105 ROWAYTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001454123</rptOwnerCik>
            <rptOwnerName>Gray Adam</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>105 ROWAYTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001635060</rptOwnerCik>
            <rptOwnerName>Coliseum School Bus Holdings, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>105 ROWAYTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-09-23</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>742566</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>18.65</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Series A Convertible Cumulative Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>11.59</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-09-23</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>100000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>164.35</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>862811</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrants</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>5.75</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-09-23</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>512000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>3.575</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2016-02-26</value>
            </exerciseDate>
            <expirationDate>
                <value>2020-02-24</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>256000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">These securities were held directly by (a) Coliseum Capital Partners, L.P. (&quot;CCP&quot;), an investment limited partnership of which Coliseum Capital, LLC, a Delaware limited liability company (&quot;CC&quot;), is general partner and for which Coliseum Capital Management, LLC, a Delaware limited liability company (&quot;CCM&quot;), serves as investment adviser, (b) Coliseum Capital Partners II, L.P. (&quot;CCP2&quot; and, together with CCP, the &quot;Funds&quot;), an investment limited partnership of which CC is general partner and for which CCM serves as investment adviser, (c) Coliseum School Bus Holdings, LLC (&quot;CSB&quot;) and (d) a separate account investment advisory client of CCM (the &quot;Separate Account&quot;).</footnote>
        <footnote id="F2">Christopher Shackelton (&quot;Shackelton&quot;) and Adam Gray (&quot;Gray&quot;) are managers of CCM and CC. CSB is a company through which CCP, CCP2 and Separate Account previously invested in the Issuer's 7.625% Series A Convertible Cumulative Preferred Stock (the &quot;Series A Convertible Cumulative Preferred Stock&quot;). CCM is the manager of CSB.</footnote>
        <footnote id="F3">The Series A Convertible Cumulative Preferred Stock is convertible into common stock at any time and has no expiration state.</footnote>
        <footnote id="F4">CCP, CCP II, CSB, and the Separate Account (each a &quot;Seller&quot;, and collectively, the &quot;Sellers&quot;) entered into a Securities Purchase Agreement (the &quot;Purchase Agreement&quot;) on September 23, 2017, pursuant to which the Sellers agreed to sell and the Issuer agreed to purchase all of (i) the shares of common stock, par value $0.0001 (the &quot;Common Stock&quot;) of the Issuer, (ii) the shares of the Issuer's Series A Convertible Cumulative Preferred Stock, par value $0.0001 per share, and (iii) the warrants to acquire Common Stock, in each case, owned by the Sellers.</footnote>
        <footnote id="F5">Following the transactions reported herein, CCP, CCP2, the Separate Account and CSB each directly owned zero (0) shares of the Common Stock, respectively.</footnote>
        <footnote id="F6">Following the transactions reported herein, CSB directly owned zero (0) shares of the Series A Convertible Cumulative Preferred Stock.</footnote>
        <footnote id="F7">Following the transactions reported herein, CCP, CCP2 and the Separate Account each directly owned zero (0) warrants, respectively.</footnote>
    </footnotes>

    <remarks>Adam Gray is a director of the Blue Bird Corporation (the &quot;Issuer&quot;). As a result, the following persons may be deemed directors by deputization of the Issuer solely for purposes of Section 16 of the Securities Exchange Act of 1934, as amended: Coliseum Capital Management, LLC; Coliseum Capital, LLC; Coliseum Capital Partners, L.P.; Coliseum Capital Partners II, L.P.; Coliseum School Bus Holdings, LLC and Christopher Shackelton.</remarks>

    <ownerSignature>
        <signatureName>Coliseum Capital Management, LLC By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-09-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Christopher Shackelton By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-09-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum Capital, LLC By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-09-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum Capital Partners, L.P. By: Coliseum Capital, LLC, its General Partner, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-09-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum Capital Partners II, L.P. By: Coliseum Capital, LLC, its General Partner, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-09-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Adam Gray, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-09-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum School Bus Holdings, LLC By: Coliseum Capital Management, LLC, its Manager By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-09-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
